无压气体动力学方程组二维Riemann问题的泛函解

TWO DIMENSIONAL RIEMANN PROBLEM FOR PRESSURELESS GAS DYNAMICS EQUATIONS WITH FUNCTIONAL SOLUTIONS

考虑无压气体动力学方程组二维Ｒｉｅｍａｎｎ问题，构造了分片常初值时的Ｒｉｅｍａｎｎ解，得出非古典激波出现在某些Ｒｉｅｍａｎｎ解中；同时给出了Ｄｉｒａｃ激波的熵条件，得出包含Ｄｉｒａｃ激波的Ｒｉｅｍａｎｎ解不唯一．

The Riemann problem for a two dimensional hyperbolic system of pressureless gas dynamics equations was considered. Riemann solutions were constructed for any piecewise constant initial data having two discontinuity rays with the origin as vertex. Non classical waves (labelled as Dirac shoch waves) appeared in some solutions. The entropy conditions for the Dirac shock waves were given, and uniqueness of Riemann solutions containing Dirac shock waves failed.